Irreversibilities and Nonidealities in Desalination Systems. Karan H. Mistry

Transcription

1 Irreversibilities and Nonidealities in Desalination Systems by Karan H. Mistry S.M., Mechanical Engineering Massachusetts Institute of Technology, Cambridge, 2010 B.S., Mechanical Engineering University of California, Los Angeles, 2008 Submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2013 c Massachusetts Institute of Technology All rights reserved. Author Department of Mechanical Engineering May 20, 2013 Certified by John H. Lienhard V Collins Professor of Mechanical Engineering Thesis Supervisor Accepted by David E. Hardt Chairman, Committee on Graduate Students

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3 Irreversibilities and Nonidealities in Desalination Systems by Karan H. Mistry Submitted to the Department of Mechanical Engineering on May 20, 2013, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical Engineering Abstract Energy requirements for desalination systems must be reduced to meet increasing global demand for fresh water. This thesis identifies thermodynamic limits for the energetic performance of desalination systems and establishes the importance of irreversibilities and solution composition to the actual performance obtained. Least work of separation for a desalination system is derived and generalized to apply to all chemical separation processes driven by some combination of work, heat, and chemical energy (fuel) input. At infinitesimal recovery, least work reduces to the minimum least work of separation: the true exergetic value of the product and a useful benchmark for evaluating energetic efficiency of separation processes. All separation processes are subject to these energy requirements; several cases relevant to established and emerging desalination technologies are considered. The effect of nonidealities in electrolyte solutions on least work is analyzed through comparing the ideal solution approximation, Debye-Hückel theory, Pitzer s ionic interaction model, and Pitzer-Kim s model for mixed electrolytes. Error introduced by using incorrect property models is quantified. Least work is a strong function of ionic composition; therefore, standard property databases should not be used for solutions of different or unknown composition. Second Law efficiency for chemical separation processes is defined using the minimum least work and characterizes energetic efficiency. A methodology is shown for evaluating Second Law efficiency based on primary energy inputs. Additionally, entropy generation mechanisms common in desalination processes are analyzed to illustrate the effect of irreversibility. Formulations for these mechanisms are applied to six desalination systems and primary sources of loss are identified. An economics-based Second Law efficiency is defined by analogy to the energetic parameter. Because real-world systems are constrained by economic factors, a performance parameter based on both energetics and economics is useful. By converting all thermodynamic quantities to economic quantities, the cost of irreversibilities can be compared to other economic factors including capital and operating expenses. By applying these methodologies and results, one can properly characterize the energetic performance and thermodynamic irreversibilities of chemical separation 3

4 processes, make better decisions during technology selection and design of new systems, and critically evaluate claimed performance improvements of novel systems. Thesis Supervisor: John H. Lienhard V Title: Collins Professor of Mechanical Engineering 4

5 Acknowledgments The work presented in this thesis could not have been completed without the help and support of many individuals; I am extremely grateful for the guidance, advice, and support that I have received during my time at MIT. Professor John Lienhard, I owe you my deepest thanks for your continued support and encouragement over the past five years. Through your guidance, I have grown as a scientist, an engineer, and most importantly, as an analytical problem solver. In addition to my adviser, I am thankful for the feedback and guidance I have received from my doctoral committee: Alexander Mitsos, Evelyn Wang, and Mostafa Sharqawy. To all the members of our research group and the Rohsenow Kendall Heat Transfer Laboratory, and in particular, Ed, Prakash, Greg, Ronan, Jacob, and Leo, thank you for providing years worth of both intellectual discourse and lighthearted banter. I have truly enjoyed my time with the group and have found our interactions both intellectually stimulating and personally rewarding. To my family, Shaila and Hemant Mistry and Priyanjali Shah, thank you for always believing in me, and more importantly, for always being there to give me a kick in the right direction whenever I need it. I have been blessed with having a number of extremely close friends. Nick, working with you, both at UCLA and at MIT, has been an absolute pleasure. You were the first of my friends to truly challenge and push me academically and I eagerly look forward to any future projects we may have together. Ben and Amneet, you both have been invaluable in helping me deal with all of the challenges that life has thrown my way. I would like to thank the King Fahd University of Petroleum and Minerals for funding the research reported in this thesis through the Center for Clean Water and Clean Energy at MIT and KFUPM under project number R13-CW-10. Lastly, thank you to everyone that I have had the pleasure of working with while at MIT, including students, faculty, and staff, for making the past five years memorable. While I know I will miss MIT dearly, as this chapter of my life comes to a close, I am excited to see where the next chapter will lead me... Karan (Rao) Mistry 5

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7 The future belongs to those who can manipulate entropy; those who understand but energy will be only accountants. Frederic Keffer Day after day, day after day, We stuck, nor breath nor motion; As idle as a painted ship Upon a painted ocean. Water, water, every where, And all the boards did shrink; Water, water, every where, Nor any drop to drink. Samuel Taylor Coleridge The Rime of the Ancient Mariner 7

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9 Contents Abstract 3 Acknowledgments 5 Contents 9 List of Figures 13 List of Tables 15 Nomenclature 17 1 Introduction The growing water problem Current state of desalination research Energy requirements for desalination systems Research objectives and thesis overview Generalized least energy of separation Nonidealities in electrolyte solutions Second Law efficiency for separation processes Economic Second Law efficiency Generalized least energy of separation Introduction Least work and least heat of separation Generalized least energy of separation Least work of separation Least heat of separation Least chemical energy (fuel) of separation Combustion Chemical disequilibrium Electrochemical reactions Limitations Least work of separation with an assist stream Conclusions

10 3 Nonidealities in electrolyte solutions Introduction Essential chemical thermodynamics Solvent Solutes Evaluation of activity coefficients Ideal solution Debye-Hückel theory and the Davies equation Pitzer ion interaction model for single electrolytes Pitzer-Kim model for mixed electrolytes Pitzer model with effective molality for mixed electrolytes Experimental data Empirical correlations Least work of separation Summary of derivation Mass basis Mole basis Feed water composition Aqueous sodium chloride Least work for an NaCl solution Error associated with ideal behavior approximation Mock seawater High valence electrolyte solution Comparison to seawater Conclusions Second Law efficiency for separation processes Introduction Energetic performance parameters Exergetic value of product Second Law efficiency for a chemical separator Second Law efficiency for a desalination system operating as part of a cogeneration plant Desalination powered by work Desalination powered by heat Desalination powered by cogenerated heat and work Analysis of entropy generation mechanisms Flashing Flow through an expansion device without phase change Pumping and compressing Approximately isobaric heat transfer process Thermal disequilibrium of discharge streams Chemical disequilibrium of concentrate stream Application to desalination technologies Multiple effect distillation

11 4.7.2 Multistage flash Direct contact membrane distillation Mechanical vapor compression Reverse osmosis Humidification-dehumidification Conclusions Economic Second Law efficiency Introduction Second Law efficiency for a chemical separator Derivation of an economics-based Second Law efficiency Minimum cost of producing product Actual cost of producing product Generalized to cogeneration systems Application to various desalination systems Multistage flash and multiple effect distillation Reverse osmosis Membrane distillation Conclusions Conclusions Generalized least energy of separation Nonidealities in electrolyte solutions Second Law efficiency for separation processes Economic Second Law efficiency Implications A Multiple effect distillation modeling 173 A.1 Introduction A.2 Overview of multiple effect distillation and review of existing models. 177 A.2.1 El-Sayed and Silver A.2.2 Darwish et al A.2.3 El-Dessouky and Ettouney Basic Model A.2.4 El-Dessouky and Ettouney Detailed Model A.3 An improved MED model A.3.1 Approximations A.3.2 Software and solution methodology A.3.3 Physical properties A.3.4 Component models A.3.5 MED-FF with flash box regeneration system model A.4 Parametric comparison of MED models A.4.1 Effect of number of effects A.4.2 Effect of steam temperature A.4.3 Effect of recovery ratio A.5 Main findings and key results

12 B Useful conversions 203 C List of Publications 205 C.1 Publications C.2 Conferences C.3 Patents Bibliography

13 List of Figures 1-1 Installed desalination capacity by technology Control volume of a work driven black box separator Control volume for evaluation of least work of separation Control volume for evaluation of least heat of separation Control volume for evaluation of least energy of separation Control volume for a black box separator powered by work Least work of separation as a function of salinity and recovery ratio Control volume for a black box separator powered by heat Least heat of separation as a function of salinity and recovery ratio Maximum gained output ratio (GOR) for desalination processes Control volume for a black box separator powered by fuel Least fuel of separation as a function of fuel type and recovery ratio Least mass of salt for separation as a function of recovery ratio Schematic diagram of reverse osmosis with forward osmosis Control volume for black box separator with salinity gradient engine Least work with an assist stream of varying mass flow rate Least work with an assist stream of varying salinity Rational activity coefficient for aqueous NaCl Rational activity coefficient for aqueous MgCl Rational activity coefficient for aqueous Na 2 SO Rational activity coefficient for NaCl in H 2 O H 2 O data for NaCl solution Control volume of a work driven black box separator Least work of separation for an NaCl solution Ideal part of the least work of separation for an NaCl solution Nonideal part of the least work of separation for an NaCl solution Percent relative error in least work of separation for aqueous NaCl The least work of separation for mock seawater solution Relative error in least work of separation for mock seawater Rational activity coefficients for species in a mock seawater solution The least work of separation for a mixture of MgSO 4 and ZnSO Relative error in least work for a mixture of MgSO 4 and ZnSO The least work of separation for various mixed electrolute solutions The least work of separation for various single electrolute solutions

14 4-1 Schematic diagram of combined water and power cogeneration Second Law efficiency of a work-driven desalination system Second Law efficiency of a heat-driven desalination system Second Law efficiency of a heat- and work-driven system Entropy generation due to temperature disequilibrium Schematic diagram of an MED system Entropy generation in an MED system Relative entropy generation in an MED system Schematic diagram of an MSF system Entropy generation in an MSF system Relative entropy generation in an MSF system Schematic diagram of a DCMD system Relative entropy generation in a DCMD system Schematic diagram of an MVC system Relative entropy generation in an MVC system Schematic diagram of an RO system Relative entropy generation in an RO system Schematic diagram of an HDH system Relative entropy generation in an HDH system Gained output ratio versus Second Law efficiency for HDH cycles Comparison of Second Law efficiency of several desalination systems Control volume for evaluation of least work of separation MSF and MED cost breakdown MSF and MED cost breakdown with entropy generation isolated Schematic diagram of an RO system RO cost breakdown RO cost breakdown with entropy generation isolated Schematic diagram of a DCMD system DCMD cost breakdown DCMD cost breakdown with entropy generation isolated A-1 Schematic diagram of a forward feed MED system A-2 Detailed MED flow diagram A-3 Control volume of an MED effect A-4 Control volume of an MED flash box A-5 Control volume of an MED feed heater A-6 MED performance ratio versus number of effects A-7 MED specific area versus number of effects A-8 MED specific area versus number of effects (2) A-9 MED performance ratio versus steam temperature A-10 MED specific area versus steam temperature A-11 MED performance ratio versus recovery ratio A-12 MED specific area versus recovery ratio

15 List of Tables 2.1 Chemical exergy of select fuels Constants and chemical data Ionic composition of natural waters Substitute ocean water recipe Ideal and nonideal parts of the least work for aqueous NaCl Second Law efficiency for various experimental desalination systems Representative values of reference state constants MSF-OT Plant Outputs MVC design inputs MVC model outputs Breakdown of costs for an MSF and MED system Energy requirements for a reverse osmosis system Cost of components required for a reverse osmosis system Capital expenses for a reverse osmosis system Replacement rate for various reverse osmosis components Operating expenses for a reverse osmosis system Energy requirements for a DCMD system Capital expenses for a DCMD system Operating expenses for a DCMD system

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17 Nomenclature Roman symbols Units A Annualized cost $/yr A Debye-Hückel constant kg 1 2 /mol 1 2 A φ Pitzer constant kg 1 2 /mol 1 2 a activity - B membrane distillation coefficient kg/(m 2 Pa s) b Davies constant kg/mol C cost $ c specific heat J/(kg K) c i cost of energy $/i c p specific heat at constant pressure J/(kg K) D i distillate from effect i kg/s D f,i distillate from flashing in effect i kg/s D fb,i distillate from flashing in flash box i kg/s d ch flow channel depth m E electromotive force V Ė Energy flow rate J/s e electron charge C F Faraday constant C/mol G Gibbs free energy J Ġ Gibbs free energy flow rate J/s g specific Gibbs free energy J/kg ḡ molar Gibbs free energy J/mol Ḣ enthalpy flow rate J/s h specific enthalpy J/kg h molar enthalpy J/mol h fg latent heat of vaporization J/kg I current A I m molal ionic strength mol/kg i interest rate % K eq equilibrium constant - K sp solubility constant - L length m M molecular weight kg/mol m molality mol solute /kg solvent 17

18 ṁ mass flow rate kg/s m i molality of species i mol/kg N number of moles mol Ṅ mole flow rate mol/s N a Avogadro s number 1/mol n number of moles mol n number of effects or stages - n number of species - n plant lifetime yr n e number of electrons - p pressure Pa Q reaction quotient - Q rate of heat transfer J/s R gas constant J/(mol K) R R replacement rate % r recovery ratio, mass basis kg product /kg feed r recovery ratio, mole basis mol H2 O product/mol H2 O feed S entropy J/K Ṡ entropy flow rate J/(s K) Ṡ gen rate of entropy generation J/(s K) S gen specific entropy generation per unit water produced J/(kg K) s specific entropy J/(kg K) s molar entropy J/(mol K) s gen specific entropy generation J/(kg K) T temperature K t time s U internal energy J V volume m 3 V volumetric flow rate m 3 /s v specific volume m 3 /kg Ẇ rate of work transfer J/s w mass fraction kg/kg w specific work transfer J/kg w width m x mole fraction mol/mol x quality kg/kg y salinity (TDS) kg solutes /kg solution Z generalized compressibility - z valence of ion - Greek Units γ f fugacity coefficient - γ i molal activity coefficient of species i - γ i cost scaling function $/m 3 γ m molal activity coefficient - 18

19 γ x rational activity coefficient - change in a variable ɛ 0 permittivity of free space F/m ɛ r relative permittivity/dielectric constant - ζ reaction coordinate - η First Law efficiency - η e isentropic efficiency of expander - η p isentropic efficiency of pump/compressor - η pp Second Law efficiency of power plant - η II Second Law/exergetic efficiency - η II,$ Economics-based Second Law efficiency - µ i chemical potential J/mol ν stoichiometric coefficient - Ξ exergy J Ξ exergy flow rate J/s ξ specific exergy J/kg ξ molar exergy J/mol ρ density kg/m 3 φ molal osmotic coefficient - φ i cost scaling function - Subscripts + cation anion ± mean ionic property 0 solvent 0 dead state 1, 2 states 1 and 2 A, a anion a assist atm atmospheric C, c cation c concentrate ch chemical d desalination plant e electricity e environment f feed f flashing H high temperature reservoir h heat i species (solvent or solutes) i state in input j stream 19

20 least m p pp r ref rev s s sep sw w x reversible process in which all process streams cross the system boundary at the RDS molal basis product power plant reaction reference reversible electrolyte salt species steam separation seawater water rational (mole fraction) basis Superscripts stream before exiting CV reference/standard state HX heat exchanger IF incompressible fluid IG ideal gas min minimum value at infinitesimal recovery rev reversible s isentropic Acronyms Units AF availability factor % BH brine heater CAOW closed air open water CAPEX capital expenses $ CD chemical disequilibrium DCMD direct contact membrane distillation DHLL Debye-Hückel Limiting Law ED electrodialysis ERD energy recovery device ERI Energy Recovery Inc. FF forward feed GOR gained output ratio - HDH humidification-dehumidification HP high pressure LHS left hand side MD membrane distillation MED multiple effect distillation MSF multistage flash MVC mechanical vapor compression 20

21 OPEX operating expenses $ OT once through ppm parts per million mg solute /kg solution ppt parts per thousand g solute /kg solution PR performance ratio PRO pressure retarded osmosis PV photovoltaic PX pressure exchanger RDS restricted dead state RED reverse electrodialysis RHS right hand side RO reverse osmosis SEC specific electricity consumption kwh e /m 3 SGE salinity gradient engine SWRO seawater reverse osmosis TD temperature disequilibrium TDS total dead state TDS total dissolved solids kg solute /kg solution TOTEX total expenses $ TTD terminal temperature difference K WH water heated 21

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23 Chapter 1 Introduction 1.1 The growing water problem Current state of desalination research Energy requirements for desalination systems Research objectives and thesis overview Generalized least energy of separation Nonidealities in electrolyte solutions Second Law efficiency for separation processes Economic Second Law efficiency The growing water problem Growing water demand due to rising population, increasing standards of living, industrialization, changing climate, and, in some instances, wasteful water use and management policies is resulting in substantial water shortage and scarcity. While developing countries are often hardest hit by lack of water supply, developed countries have had to face these issues as well [1, 2]. The United Nations World Water Development Report states that as of 2003, over one billion people lack access to adequate drinking water [3]. According to UNICEF, nearly 5,000 children die every day as a result of unsafe water as of 2006 [4]. Unfortunately, as the world population continues to increase and as water supplies continue to be contaminated, it is clear that the current water situation is only going to get much worse. In order to address the worsening water situation, one of the Millennium Development Goals from a UN Summit in 2000 was to halve the population of people without access to safe drinking water [3]. Traditionally, fresh water has been obtained from various fresh water sources including lakes, rivers, and aquifers. In water-scarce locations, water is often transported great distances at great costs (examples include Southern California [5] and 23

24 24 CHAPTER 1. INTRODUCTION Other 2% Electrodialysis 3 % Hybrid 1% Reverse osmosis 63% Multiple effect distillation 8% Installed capacity 74.8 million m 3 /d Multistage flash 23% Figure 1-1: Installed desalination capacity by technology, as of 2013 [11]. Northern China [6]). As the demand for freshwater increases, these water sources are increasingly being taxed, often to the point of near-exhaustion. Unquestionably, new water sources must be found in order to alleviate demand. Fortunately, desalination (and in particular, seawater desalination) opens up the oceans a new and essentially unlimited and renewable source of freshwater. Desalination has been practiced for over a century as sailors used to evaporate seawater into pieces of cloth and then squeeze the freshwater out to consume [7]. Basic solar stills were also used (and still are for niche applications) to produce limited amounts of water [8]. However, substantial research in desalination technologies has occurred in recent decades in order to develop more efficient and economical methods, both to meet growing needs for potable water and to remediate industrial process waters [9, 10]. In the last years, modern engineering has resulted in the development of substantially improved desalination techniques that can produce water efficiently and economically. As of 2013, there is nearly 75 million m 3 /d of installed desalination capacity [11]. These plants treat a broad range of waters including seawater, river water, ground water, and others. In general, the various desalination technologies can be divided into two basic categories based on the method of separation: thermal (distillation) processes and mechanical (typically membrane) processes [12]. Thermal-based processes include multistage flash (MSF), multiple effect distillation (MED), humidification-dehumidification (HDH), vapor compression (VC), and membrane distillation (MD). Mechanical processes include reverse osmosis (RO), forward osmosis (FO), and electrodialysis (ED). Figure 1-1 shows the installed capacity of each of the major desalination technologies. 1.2 Current state of desalination research Two major limiting phenomenological factors affect the design and operation of desalination plants: energy consumption and scale formation [7]. Techniques have been developed to address both these issues.

25 1.2. CURRENT STATE OF DESALINATION RESEARCH 25 Energy consumption is typically minimized by trying to maximize energy recovery. In thermal desalination plants, energy is carried in feed, product, and concentrate (brine) streams in the form of thermal energy. Energy can be recovered through the use of multiple effects (or stages), preheaters, and regenerators. In each effect of an MED plant, the heat of vaporization released during condensation of the vapor stream is used to evaporate more water from the brine stream. Regenerators are used to exchange thermal energy from the warm brine and vapor streams to the cold feed water stream. In each stage of an MSF plant, the heat of vaporization is used to preheat the feed seawater stream through the process of condensation. In both types of plants, increased number of effects (or stages) results in increased energy reuse, resulting in lower energy consumption per unit water produced [13]. Reverse osmosis implements energy recovery in a very different way. Since most of the energy in RO is stored in the mechanical form of a compressed liquid, advanced pressure exchangers are used to transfer energy from the high pressure brine stream to the lower pressure feed stream [14, 15]. Recent developments of pressure exchangers by companies such as Energy Recovery, Inc. (ERI) have greatly increased the efficiency of energy recovery in RO systems and have substantially reduced the net energy cost. While energy recovery can greatly reduce the energy consumption of a desalination plant, substantial savings can come through the use of water and power cogeneration. It is especially advantageous to run thermal power plants in a cogeneration configuration since they are readily powered using waste heat or steam bled from the last stages of a turbine. Cogeneration can reduce the required energy input by approximately a third [12, 16]. Because of this energy savings, cogeneration is already common practice for large-scale seawater desalination plants, especially MSF and MED which are most common in the Gulf region (approximately 94% of production) where fuel is inexpensive and the additional cost of running the cogeneration plants is minimal [17]. Reverse osmosis is typically powered using electricity from the grid or from a dedicated power plant. In addition to minimizing energy consumption, reducing the potential for scale formation is also essential when trying to design efficient desalination systems. In thermal plants, scaling greatly reduces heat transfer performance, requiring larger heat transfer surface area; and it limits the maximum brine temperature, which lowers the maximum possible thermodynamic efficiency. In membrane plants, scaling and fouling can block or damage the membranes, requiring down time and even expensive repair or replacement costs [7, 18]. Scale formation, fouling, and deposit build up can be controlled and prevented in three different ways. First, pretreatment can be used to remove dissolved and suspended solids through processes such as softening, ion exchange, filtration, flocculation, coagulation, and dispersion. Next, various chemical treatments, such as scale inhibitors and antifoulants, can be used to try to prevent deposition build up. Finally, if scaling and fouling has occurred, the deposits can be periodically removed through chemical and/or mechanical processes [19]. Through proper pretreatment, the concentration of the major scaling components (divalent ions such as calcium, magnesium, carbonate, and sulfate) can be reduced. By removing the major scaling and fouling agents, the top brine temperature can be raised by as much as 10 K, thus increasing the

26 26 CHAPTER 1. INTRODUCTION Ẇ sep Q 0, T 0 Feed (f) Black Box Separator Product (p) Concentrate (c) Figure 1-2: A control volume representation of a desalination system is used to derive the least work of separation. thermodynamic efficiency. Nanofiltration has proven to be particularly successful in this application [20]. In order to assess the potential for scale formation, it is essential to understand the water chemistry of the feed water. 1.3 Energy requirements for desalination systems As discussed previously, minimizing energy consumption is one of the primary goals when designing a chemical separation process. While any sort of energy improvements must be balanced with the additional cost required to achieve said improvement, it is still useful to analyze the energy requirements at a fundamental level and independently of the economic issues. In Chapter 2, a control volume approach is used to derive an expression for the work of separation requirements for an arbitrary black box chemical separator, as illustrated in Fig By applying the First and Second Laws of Thermodynamics to the control volume and combining them subject to several requirements discussed in Chapter 2, the power required to drive the separation process is found to be: Ẇ sep = Ġp + Ġc Ġf + T 0 Ṡ gen (1.1) where Ġi is the flow rate of Gibbs free energy of stream i, T 0 is the environment temperature at which heat transfer occurs, and Ṡgen is the entropy generated during the chemical separation process. When Eq. (1.1) is evaluated per unit flow rate of product, it represents the work of separation. Equation (1.1) can be divided into two parts that are quite distinct and can be studied independently of one another. The first part is a function of the Gibbs free energy of each of the process and streams and is typically referred to as the least work of separation when it is evaluated for unit product mass flow rate: Ẇ least = Ġp + Ġc Ġf (1.2) The least work of separation is purely a function of the composition of each of the process streams (in this case, feed, product, and concentrate) and the recovery ratio with which the separation process is performed. Therefore, in order to fully understand all of the nuances of Ẇ least, it is important to study the chemistry of the various solutions being treated.

27 1.4. RESEARCH OBJECTIVES AND THESIS OVERVIEW 27 The second part is a function of the irreversibilities that occur during the separation process and is often referred to as the exergy destroyed: Ξ destroyed = T 0 Ṡ gen (1.3) Exergy destruction in chemical separation processes is largely not a function of chemistry. While there is some entropy generated during mixing (which is a function of chemistry), the largest sources of entropy generation tend to be heat transfer across finite temperature differences for thermal systems and viscous losses for membrane systems. Therefore, the exergy destruction part of the work of separation can be best understood by analyzing the various sources of irreversibility within a system. 1.4 Research objectives and thesis overview Given the importance of reducing energy consumption for any process, the primary goal of this thesis is to develop a deeper understanding of the fundamental sources of energy requirements involved in chemical separation processes, and in particular, desalination technologies. As a result, there are four primary areas that are investigated: 1. Work of separation requirements, generalized to any type of energy input. 2. Effect of solution composition and chemistry on the least work of separation. 3. Effect of irreversible processes on the increase in work requirements. 4. Cost of thermodynamic irreversibilities as compared to other economic factors. In addition to these four areas, a detailed analysis of MED models as well as the development of a novel model is included in Appendix A. While this thesis is written in such a way that each chapter builds off of the previous chapters, care has been taken to ensure that each chapter can be read largely independently of the others. Therefore, major derivations are briefly summarized in relevant chapters as appropriate Generalized least energy of separation Equation (1.1) is a useful expression for evaluating the work requirements for a desalination process that is powered purely using work. However, many modern systems require some combination of work, heat, and chemical fuel as energy input. Chapter 2 focuses on the development of a generalized equation for calculating the energy of separation requirements for an arbitrary chemical separator that is powered by any type of energy input. Additionally, special cases of the generalized equation, including the least work of separation, least heat of separation, and least fuel of separation are analyzed and compared [21, 22] Nonidealities in electrolyte solutions Chemical composition plays a large role in the magnitude of the least work of separation. As a result, standard seawater properties and pure water properties cannot be used for arbitrary source waters that may be composed of very different species. Since

28 28 CHAPTER 1. INTRODUCTION standard datasets do not exist for all solutions that might be considered, physical properties must be evaluated using thermodynamic models. The thermodynamic models are typically composed of two parts, an ideal part that is a function of mole fractions, and a nonideal part that is a function of activity coefficients that represent nonideal solution behavior. Incorrectly using the various models to calculate the nonidealities can result in substantial error in the evaluation of the least work of separation. Chapter 3 focuses on the evaluation of activity coefficients for both single and mixed electrolyte solutions and highlights the importance of considering chemical composition as well as correct usage of existing models [23 25] Second Law efficiency for separation processes For most real-world desalination systems, exergy destruction will be several times larger than the least work of separation. Therefore, understanding the irreversibilities within a given system is essential for reducing the overall energy requirements. In Chapter 4, all of the major entropy generation mechanisms present in desalination systems are investigated. The resulting expressions are applied to six different desalination technologies in order to show the primary source of losses in each type of system. In addition to looking at the sources of entropy generation, Second Law efficiency for chemical separation processes is formally defined. This requires identifying the exergetic value of the product water and all sources of losses. The definition of Second Law efficiency is then applied to the same six technologies. Additionally, it is used for desalination systems that are operating in a cogeneration scheme with a power plant [21, 22] Economic Second Law efficiency Real-world systems are ultimately constrained primarily by economic factors; therefore, it is useful to have a performance parameter that can adequately capture both energetic and economic effects. An economics-based Second Law efficiency is defined by analogy to the energetic parameter in order to characterize energetics and economics. By converting all thermodynamic quantities to economic terms, it is found that the cost of irreversibilities can be compared to other important economic factors including capital and operating expenses [26].

29 Chapter 2 Generalized least energy of separation 2.1 Introduction Least work and least heat of separation Generalized least energy of separation Least work of separation Least heat of separation Least chemical energy (fuel) of separation Combustion Chemical disequilibrium Electrochemical reactions Limitations Least work of separation with an assist stream Conclusions Chapter abstract Increasing global demand for fresh water is driving the development and implementation of a wide variety of seawater desalination technologies driven by different combinations of work, heat, and chemical energy. A consistent basis for comparing the energy consumption of such technologies through the minimum least energy of separation, a parameter that is analogous to Carnot efficiency for power plants, is developed in this chapter. A generalized expression for the least energy of separation is derived for generic chemical separators. The generalized equation is then evaluated through a parametric study considering work input, heat inputs at various temperatures, and various chemical fuel inputs. This chapter consists of work that is published in [21, 22]. 29

30 30 CHAPTER 2. GENERALIZED LEAST ENERGY OF SEPARATION 2.1 Introduction Currently, several different technologies for desalinating water are in wide use, including reverse osmosis (RO), multistage flash (MSF), multiple effect distillation (MED), among others. These systems are typically powered by electricity (work), heat, fuel, or some combination thereof. The description of energy requirements becomes more complicated when one considers that many larger scale water plants are operated in conjunction with power plants in a cogeneration scheme [16]. While advances over the last several decades have resulted in dramatically reduced energy utilization, desalination is still energy intensive, and it is important to be able to fully characterize the performance of these systems and to compare the relative energy costs from system to system. Understanding the fundamental thermodynamic limits on energy requirements is essential in this characterization. The least work of separation (Ẇleast) represents the least amount of work required to reversibly separate a single stream into multiple streams of different composition [16, 21, 22, 27 29]. Similarly, the least heat of separation ( Q least ) can be used to represent the least amount of heat required for a separation process. Both are benchmarks to which desalination systems are compared, much as Carnot efficiency is the ideal benchmark to which power plants are compared. While the least work and least heat of separation are useful parameters for work and heat driven systems respectively, it is difficult to directly compare the energies represented by least work and least heat. Additionally, these parameters are only useful for systems that have a single energy source (work or heat only). Many modern separation processes, including most thermal desalination systems (e.g., MSF and MED), require both thermal and mechanical energy input. Still other systems may be powered by chemical energy. Therefore, a more useful least energy metric would capture simultaneous mechanical, thermal, and chemical energy inputs. This chapter is based on the work of Mistry et al. [21, 25]. First, the least work and least heat equations are derived from simplified control volumes. Then, the calculation is generalized to consider the least energy of separation for a generic chemical separator. A least separation process is defined here as a completely reversible process in which the minimum amount of energy, as required by the Second Law of Thermodynamics, is needed to drive a chemical separation process. This concept is clarified and further developed through several examples. In Chapter 4, the generalized least energy of separation concept is developed further and is used to define the Second Law efficiency of a generic chemical separator. 2.2 Least work and least heat of separation Consider a simple black-box separator model for a desalination system, with a separate control volume surrounding it at some distance, as shown in Fig The work of separation entering the system is denoted by Ẇsep and the heat transfer into the system is Q. Stream f is the incoming feed, stream p is pure water (product), and stream c is the concentrate (brine). By selecting the control volume sufficiently far from the

31 2.2. LEAST WORK AND LEAST HEAT OF SEPARATION 31 Ẇ sep Q 0, T 0 Feed (f) T f = T 0 T f Black Box Separator T p T c Product (p) T p = T 0 Concentrate (c) T c = T 0 Figure 2-1: When the control volume is selected suitably far away from the physical system, all inlet and outlet streams are at ambient temperature and pressure. The temperature of the streams inside the control volume (T i ) might not be at T 0. physical plant, all the inlet and outlet streams enter and leave the control volume at ambient temperature (T 0 ) and pressure (p 0 ) but at different chemical composition. Additionally, the heat transfer occurs at ambient temperature. The logic underlying this latter formulation is that the exergy of the outlet streams attributable to thermal disequilibrium with the environment is not deemed useful. In other words, the purpose of a desalination plant is to produce pure water, not pure hot water. Consider separately the thermal conditions at the desalination system boundary (solid box) and the distant control volume boundary (dashed box). Product and reject streams may exit the desalination system at temperatures T p and T c, different than ambient temperature, T 0. The exergy associated with these streams could be used to produce work that would offset the required work of separation. However, if the exergy associated with thermal disequilibrium is not harnessed in this way, but simply discarded, entropy is generated as the streams are brought to thermal equilibrium with the environment. This entropy generation is analyzed in Section Similarly, pressure disequilibrium would result in additional entropy generation [30]. In general, differences in concentration between the various streams represent a chemical disequilibrium which could also be used to produce additional work; however, since the purpose of the desalination plant is to split a single stream into two streams of different concentrations (i.e., product water is not in chemical equilibrium with the feed or environment), the outlet streams are not brought to chemical equilibrium with the environment. The least work and least heat of separation are calculated by evaluating the First and Second Laws of Thermodynamics for the distant control volume. The convention that work and heat input to the system are positive is used. Ẇ sep + Q 0 + ṁ f h f = ṁ p h p + ṁ c h c (2.1) Q 0 + ṁ f s f + T Ṡgen = ṁ p s p + ṁ c s c 0 (2.2) In Eqs. (2.1) and (2.2), ṁ i, h i, and s i are the mass flow rate, specific enthalpy and specific entropies of the feed (f), product (p), and concentrate (c) streams. The First and Second Laws are combined by multiplying Eq. (2.2) by ambient temperature, T 0, and subtracting from Eq. (2.1) while noting that the specific Gibbs free energy is,

32 32 CHAPTER 2. GENERALIZED LEAST ENERGY OF SEPARATION Q 0, T 0 Q sep, T H Q 0 Feed T f = T 0 T f Ẇ sep Black Box Separator T p T c Product T p = T 0 Concentrate T c = T 0 Figure 2-2: Addition of a high temperature reservoir and a Carnot engine to the control volume model shown in Fig g = h T s (all evaluated at T = T 0 ). Ẇ sep = ṁ p g p + ṁ c g c ṁ f g f + T 0 Ṡ gen (2.3) In the limit of reversible operation, entropy generation is zero and the work of separation becomes the reversible work of separation, which is also known as the least work of separation: Ẇ least Ẇ rev sep = ṁ p g p + ṁ c g c ṁ f g f (2.4) Equation (2.3) represents the amount of work required to reversibly produce pure water at a rate of ṁ p. If heat is used to power a desalination system instead of work, the heat of separation is a more relevant parameter. Recalling that heat engines produce work and reject heat, the calculation of the heat of separation is straightforward. Figure 2-2 shows the control volume from Fig. 2-1 but with a reversible heat engine providing work of separation. If the heat is provided from a high temperature reservoir, then the First Law for the heat engine is Q sep = Ẇsep + Q 0 (2.5) Assuming a reversible heat engine operating between the high temperature reservoir at T H and ambient temperature T 0 and considering work per unit mass produced, Ẇ sep ṁ p = Q sep Q 0 = Q ( sep 1 T ) 0 ṁ p ṁ p ṁ p T H (2.6) where the second equality holds as a result of the entropy transfer that occurs in a reversible heat engine operating between two heat reservoirs. Therefore, the heat of separation is: Q sep ṁ p = Ẇ sep ( ) = 1 T 0 T H ṁ p Ẇleast + T 0 Ṡ ( ) gen (2.7) 1 T 0 T H ṁ p where the second equality holds by combining Eqs. (2.3) and (2.4). Note that Eq. (2.7)

33 2.3. GENERALIZED LEAST ENERGY OF SEPARATION 33 can also be derived from Eqs. (2.1) and (2.2) if Ẇ sep is set to zero and the temperature in the Second Law is set to T H [27]. Equations for the least heat of separation, Q least and the minimum least heat of separation, Q min least can be obtained from Eq. (2.7) in the same manner as the corresponding work equations. In practice, the entropy generation term in Eqs. (2.3) and (2.7) dominates over the least work or least heat. Therefore, the parameter, Ṡ gen /ṁ p is of critical importance to the performance of desalination systems [27]. This term is referred to as the specific entropy generation, S gen, and is a measure of entropy generated per unit of water produced: S gen = Ṡgen ṁ p (2.8) In the formulation described above, all streams enter and exit the system at ambient temperature. Therefore, the specific exergy destroyed, ξ d, in the system is equal to the product of S gen and the ambient temperature. This term is physically reflective of the same phenomenon that produces Eq. (2.8): ξ destroyed = T 0Ṡgen ṁ p (2.9) While the present chapter focuses on reversible processes, entropy generation in chemical separation processes will be considered in detail in Chapter 4. Now that the least work and least heat of separation have been derived for simplified control volumes, a generalized expression is derived that is applicable to all chemical separation systems. 2.3 Generalized least energy of separation The equation for the generalized least energy of separation is derived using the generalized exergy equation for an arbitrary system control volume shown in Fig. 2-3 [31]. This control volume has q inlet streams and r outlet streams, each potentially at different temperature, pressure, and chemical composition of 0 to n species. For simplicity, kinetic and potential energy is neglected. The system is in thermal contact with p heat reservoirs and is free to transfer work (p 0 dv/dt), heat ( Q 0 ), and mass (Ṅ0,i) with the environment. In Fig. 2-3 and the subsequent equations, the subscript 0 is used to denote environmental conditions and the subscript i is used to denote a specific species (e.g., Ṅ 0,i is the mole flow rate of species i into the system, from the environment at T 0, p 0 with a chemical potential of µ 0,i ). The sign convention of positive work input is used herein. As a result, the outlet streams can leave the system at thermal, mechanical, and chemical equilibrium with the environment. That is, they can leave the system at the total dead state (TDS). The First and Second